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The compositeness test consisting of the application of Fermat's little theorem.

1 and -1 are the only integers which divide every integer. They are therefore called the prime units.

A general quadratic Diophantine equation in two variables x and y is given by ax^2+cy^2=k, (1) where a, c, and k are specified (positive or negative) integers and x and y are ...

A deeper result than the Hardy-Ramanujan theorem. Let N(x,a,b) be the number of integers in [n,x] such that inequality a<=(omega(n)-lnlnn)/(sqrt(lnlnn))<=b (1) holds, where ...

The converse of Fermat's little theorem is also known as Lehmer's theorem. It states that, if an integer x is prime to m and x^(m-1)=1 (mod m) and there is no integer e<m-1 ...

Lucas's theorem states that if n>=3 be a squarefree integer and Phi_n(z) a cyclotomic polynomial, then Phi_n(z)=U_n^2(z)-(-1)^((n-1)/2)nzV_n^2(z), (1) where U_n(z) and V_n(z) ...

A composite number n is a positive integer n>1 which is not prime (i.e., which has factors other than 1 and itself). The first few composite numbers (sometimes called ...

Thurston's conjecture proposed a complete characterization of geometric structures on three-dimensional manifolds. Before stating Thurston's geometrization conjecture in ...

The Wells graph, sometimes also called the Armanios-Wells graph, is a quintic graph on 32 nodes and 80 edges that is the unique distance-regular graph with intersection array ...

A (v,g)-cage graph is a v-regular graph of girth g having the minimum possible number of nodes. When v is not explicitly stated, the term "g-cage" generally refers to a ...